| Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate | |
| Ren, Jingli; Yuan, Qigang; Ren, JL (reprint author), Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China.; Ren, JL (reprint author), Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China. | |
| Source Publication | CHAOS
 |
| 2017-08-01 | |
| Volume | 27Issue:8 |
| ISSN | 1054-1500 |
| Abstract | A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincare map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincare map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last. Published by AIP Publishing. |
| DOI | 10.1063/1.5000152 |
| URL | 查看原文 |
| Indexed By | SCI |
| Language | 英语 |
| WOS ID | WOS:000409112600028 |
| WOS Keyword | NONLINEAR DYNAMICAL-SYSTEM ; GLYCEROL FERMENTATION ; KLEBSIELLA-PNEUMONIAE ; CLOSTRIDIUM-BUTYRICUM ; PRODUCT INHIBITION ; 1,3-PROPANEDIOL ; PATHWAY ; OSCILLATIONS ; HYSTERESIS |
| WOS Research Area | Mathematics ; Physics |
| WOS Subject | Mathematics, Applied ; Physics, Mathematical |
| Funding Organization | NSFC(11771407) ; Innovation Research Team of Science and Technology of Henan Province(17IRTSTHN007) ; Plan for Scientific Innovation Talent of Henan Province(164200510011) ; Opening fund of State Key Laboratory of Nonlinear Mechanics(LNM201710) ; National Key Research and Development Program of China(2017YFB0702500) |
| Classification | 一类 |
| Ranking | 2 |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/70042 |
| Collection | 非线性力学国家重点实验室 |
| Corresponding Author | Ren, JL (reprint author), Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China.; Ren, JL (reprint author), Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China. |
| Recommended Citation GB/T 7714 | Ren, Jingli,Yuan, Qigang,Ren, JL ,et al. Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate[J]. CHAOS,2017,27,8,. |
| APA | Ren, Jingli,Yuan, Qigang,Ren, JL ,&Ren, JL .(2017).Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate.CHAOS,27(8). |
| MLA | Ren, Jingli,et al."Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate".CHAOS 27.8(2017). |
| Files in This Item: | Download All | |||||
| File Name/Size | DocType | Version | Access | License | ||
| JouArt-2017-156.pdf（3080KB） | 期刊论文 | 作者接受稿 | 开放获取 | CC BY-NC-SA | View Download | |
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